How Compton Worked
Gamma rays pass right through mirrors, so unlike most other observatories for different wavelengths, this observatory had to use the Compton scattering effect to detect and map out high-energy gamma rays. Essentially, Compton scattering consists of when x-rays interact with ordinary matter, thus losing energy. Check out this NASA article for an explanation of how Compton scattering works for telescopes.
From here, it operated four different instruments that covered a huge portion of the electromagnetic spectrum, from 20 keV to 30 GeV - a one eV or electron volt being a unit of energy gained by an electron, which is accelerated through a potential of 1 volt, roughly equivalent to 1.6 x 10-19 Joules.
They included the BATSE, the Burst and Transient Source Experiment, which conducted full sky experiments; the OSSE, the Oriented Scintillation Spectrometer Experiment, which would do point observations of both source and background noise; the COMPTEL, the Imaging Compton Telescope; and the EGRET, the Energetic Gamma Ray Experiment Telescope, a wide field telescope that specialized in more high energy gamma rays.
Compton was set at a very low orbit, a mere 450 km, to just duck under the Van Allen radiation belt.